Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
n = int(raw_input())


def sol(nums, q):
    lo = 0
    hi = len(nums)-1
    found = False
    while lo <= hi and not found:
        mid = (hi + lo) // 2
        v = nums[mid]
        if v == q:
            found = True
        else:
            if v > q:
                hi = mid - 1
            else:
                lo = mid + 1
    return found


m = 1
nums = []
i = 1

while ((i * (i + 1)) / 2) < n:
    nums.append((i * (i + 1)) / 2)
    i += 1

i = 0
res = 'NO'
l = 0
r = len(nums) - 1

for i in range(len(nums)):
    cur = nums[i]
    found = sol(nums, n - cur)
    if found:
        res = 'YES'
        break

print(res)